Dynamics analysis and motion control for underactuated cart-double-pendulum system

A cart-double-pendulum system is a complicated nonlinear underactuated system, which has three degrees of freedom and has two control inputs. This paper discusses the dynamics analysis and motion control problems for this mechanical system. First, an input relationship is constructed by analyzing the dynamic properties of the system. It changes the system to be a nonlinear cascade system. Second, three types of control laws for the cascade system are presented based on a virtual friction idea. That makes the fixed position motion control objective of the cart-double-pendulum be achieved. Finally, numerical simulations demonstrate the effectiveness of the developed theoretical results.